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Simplifying 4v2 + -15 = -9v Reorder the terms: -15 + 4v2 = -9v Solving -15 + 4v2 = -9v Solving for variable 'v'. Reorder the terms: -15 + 9v + 4v2 = -9v + 9v Combine like terms: -9v + 9v = 0 -15 + 9v + 4v2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.75 + 2.25v + v2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + 2.25v + 3.75 + v2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + 2.25v + v2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + 2.25v + v2 = 0 + 3.75 2.25v + v2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 2.25v + v2 = 3.75 The v term is 2.25v. Take half its coefficient (1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. 2.25v + 1.265625 + v2 = 3.75 + 1.265625 Reorder the terms: 1.265625 + 2.25v + v2 = 3.75 + 1.265625 Combine like terms: 3.75 + 1.265625 = 5.015625 1.265625 + 2.25v + v2 = 5.015625 Factor a perfect square on the left side: (v + 1.125)(v + 1.125) = 5.015625 Calculate the square root of the right side: 2.239559108 Break this problem into two subproblems by setting (v + 1.125) equal to 2.239559108 and -2.239559108.Subproblem 1
v + 1.125 = 2.239559108 Simplifying v + 1.125 = 2.239559108 Reorder the terms: 1.125 + v = 2.239559108 Solving 1.125 + v = 2.239559108 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + v = 2.239559108 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + v = 2.239559108 + -1.125 v = 2.239559108 + -1.125 Combine like terms: 2.239559108 + -1.125 = 1.114559108 v = 1.114559108 Simplifying v = 1.114559108Subproblem 2
v + 1.125 = -2.239559108 Simplifying v + 1.125 = -2.239559108 Reorder the terms: 1.125 + v = -2.239559108 Solving 1.125 + v = -2.239559108 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + v = -2.239559108 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + v = -2.239559108 + -1.125 v = -2.239559108 + -1.125 Combine like terms: -2.239559108 + -1.125 = -3.364559108 v = -3.364559108 Simplifying v = -3.364559108Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.114559108, -3.364559108}
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